Such an apparatus has been described in U.S. Pat. No. 3,404,789. In this apparatus the stacks of blanks are brought successively by means of a conveyor into an unstacking station where individual blanks are lifted off the blank stack by means of hoisting mechanisms, especially suction bridges, and are transferred to a magnetically controlled suspended conveyor. From the suspended conveyor, the blanks pass via a double-blank control device into a centering station and, by way of another intermediate station provided thereafter, into the working chamber of a processing machine, for example a first press of an automated press line. The centering and intermediate stations are loaded and/or unloaded in the operating cycle of the processing machine to be supplied. If, in this apparatus, a double blank is conveyed by the suspended conveyor, then the double-blank control device responds and the double blank, deposited in the meantime in the centering station, is separated. This is accomplished by moving the centering station away by pivoting, whereby the double blank is transferred to an additional roller conveyor train and deposited on a double-blank depository. The elimination of double blanks requires, in this conventional device, an expensive construction and, furthermore, results in a production pause, since the unstacking process is controlled in direct dependence on the operating cycle of the processing machine. A further production loss is incurred due to the fact that, after a stack of blanks has been unstacked, the apparatus must be arrested until a new stack of blanks has been introduced underneath the hoisting mechanism.